It means that a person pledges during his lifetime that after death, organs from his/her body can be used for transplantation to help terminally ill patients and giving them a new lease of life.
There are two way of organ donation:

Living related donors:- Only immediate blood relations(brother,sister parents children)can donate as per the Transplantation of Human Organ Act 1994.Living donor can donate only few organs, one kidney(as one kidney is capable of maintaining the body functions),a portion of pancreas(as half ofthe pancreas is adequate for sustainingpancreatic functions)and part of the liver (as the few segments that are donated will regenerate after a period of time) can be donated.